The Railgun and her friends in Railgun S

One of the criticisms I've seen leveled at Railgun S is that Mikoto
passes up involving her friends. Evirus says:

For example, Mikoto spends most of the first cour of Railgun S
sneaking around rather than enlisting the help of her roommate, the
teleporter.

I can't say that Evirus is wrong because it's up to the show itself
to convince its audience that events make sense and clearly the show
hasn't sold Evirus on this. But what I can say is that the show did
sell me on Mikoto's actions.

(There are about to be spoilers.)

First off, let's note that Mikoto does hardly any sneaking around in the
first cour. She does about 90% of her work in a phone booth (and might
have managed to do all of it if she wasn't impatient, but then if she
had there wouldn't be much of a show) and much of the rest of it seems
to have been less 'sneaking around' and more 'walking in casually'. In
short, for almost all of the time she steamrollers everything in sight.
The only time she actually needs any help happens when actual opponents
appear (in the only actual fight) and this catches Mikoto completely by
surprise when it happens.

(The show doesn't bother spending much time showing her steamroller
stuff because it kind of lacks excitement.)

Beyond this, the show has sold me on a collection of reasons that
Mikoto doesn't and can't involve her friends, especially Kuroko.
In no particular order:

Mikoto repeatedly talks about this being her fault and her problem
to deal with. This is somewhat irrational but the show sells me on
it being her heartfelt attitude, due in part to the horror of the
situation.

The situation is genuinely horrible (and it only gets worse as it
goes along). Mikoto sees someone die in front of her and finds out
that thousands of people have been systematically killed, with more
happening every day. This is a huge trauma to dump on your middle
school friends who are enjoying an innocent life in the sunshine.
I can completely see not wanting to drag them into the nightmare.

Kuroko is effectively a member of the police and Mikoto is busy
doing all sorts of lawbreaking. It's at least uncool to ask your
police buddy to help you commit a crime; you've put them in a
really awkward spot no matter what they choose.

Mikoto is not actually a member of Judgment and Kuroko has been
shown as repeatedly trying to keep her from getting involved in
Judgment operations (generally unsuccessfully, which results in Kuroko
sighing a lot). It thus seems very likely that if Mikoto brought the
whole problem to Kuroko officially she would immediately get sidelined
(quite possibly very firmly, as Anti-Skill moved in). Mikoto is not
exactly a sideline girl.

(Of course, what we know in the first cour and what Mikoto finds out
later is that going to the authorities wouldn't help anyways. Academic
City is fundamentally corrupt and brutal.)

If confronted by a choice between friendship (to Mikoto) and duty
(to Judgment), Kuroko would probably choose duty. I say this because
shortly after the end of the first cour (if I remember episode
numbers right) the situation actually gets so bad that Mikoto probes
Kuroko about this (phrased as a hypothetical) and Kuroko gives an
unhesitating answer. Mikoto doesn't seem surprised.

(Mikoto actually seemed relieved, which felt right for me. Kuroko's
answer meant that Mikoto didn't have to even consider dragging her
friend into the darkness with her. Of course Kuroko might have made a
different choice in a non-hypothetical situation.)